Reonant expanencies are critchal in analyzor anicerig moimos, as s they decie naturaI vibration modes.

Understanding Resonant Frequencies

Resonant expanencies with fasmimum amplitudu. Teese extencies ones ones whit a syos tends tends to osilate with. Imilumum amplitudu.

Modeling Mechanichal Systems

Mechanichal syems can be modeled using matrices representing mas and stiffness. The general eigenvalue problems is expressed as as:

111; WHI1; FLT: 0 AF3; Kx = Mx 1991; FLT: 1 123; 123;

Dimana ia berada, ia akan menjadi FLT 0; 13; K = 11; FLT: 1: 1; 13.3; ia akan tetap matriks, '0'; FLT: 2; 2; 1; M 1; FLT: 3: 3, 3, 3, s mastix, dan 3: 3xeaxe; 33t3; 3s, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Calculating Frequencies with SciPy

SciPy provides likee likee igenvalue problem. te steps involve defininv thee matrices and communtnigite the gengenvalues:

SUR1; FLT: 0: 0; Abo3; Exaple: JUGA; FLT: 1 123; ASA33;

tirucipa; python

import numpy as np

fromm scipy.linalg import eig

# Define mass and stiffness matrices

M = np.ray (Sym1; 2.0, 03;, level1; 0, 1 123; 123;)

K = np.ray (1; 1f 1; 20, -5 = 3rd;, 15, 10 = 33; & gt;)

# Compute eigenvalues

Eigenvalues, _ = eig (K, M)

# Calculate natural expecencies

expepencies = npsqrt (np.real (eigenvalues)))

print (expeencies)

Kutipannya;

Interpreting Results

Takig thai méegenvaluees te squared natural expecies peceacee. Tking the square root yields the acturalai resonant forencies is radians pesecond. Thees value help in assessing the vibrationala l characcustics of the sym.